BTGModeratorVI wrote: ↑Sun Sep 27, 2020 7:10 am
Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y, working alone, to complete the entire job?
(A) 18
(B) 13 1/2
(C) 7 1/5
(D) 4 1/2
(E) 3 2/3
Answer:
A
Source: Official guide
Another way to solve this question is to
assign a nice value to the job.
So, we want to use a value that works well with the given numbers in the question (9, 3 and 4 hours).
Since 36 is the least common multiple of 9, 3 and 4, let's say the entire job consists of making
36 widgets
Machine X can complete a certain job in 9 hours
So, Machine X's RATE =
36/9 =
4 widgets per hour
Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours.
At its rate of
4 widgets per hour, Machine X would have produced 12 widgets in 3 hours
36 - 12 = 24
So, after the first 3 hours, the two machines would need to produce the
24 remaining widgets in the job
Since the two machines COMBINED produced the remaining
24 in 4 hours, their COMBINED RATE =
24/4 = 6 widgets per hour
We can write: (Machine X's rate) + (Machine Y's rate) = 6 widgets per hour
Substitute to get:
4 + (Machine Y's rate) = 6 widgets per hour
From this, we can see that Machine Y's rate =
2 widgets per hour
How many hours would it have taken machine Y, working alone, to complete the entire job?
time = output/rate
So, time =
36/
2 = 18
Answer: A
Cheers,
Brent
